A simple method for calculating the span and chordwise loading on straight and swept wings of any given aspect ratio at subsonic speeds

Abstract

The methods of classical aerofoil theory are used to derive a general theory for wings of any given plan form. Accordingly, the general downwash equation is split into two parts : one, the effective incidence, being due to the downwash induced by the vorticity component along the span; and the other, the induced incidence, which is due to the downwash induced by the streamwise vorticity component. The latter is related to the downwash in the Trefftz plane, and a downwash factor is introduced to include both the limiting cases of very small aspect ratio (Jones) and of very large aspect ratio (Prandtl). The downwash resulting from the spanwise vortices is approximated by a simple relation, the accuracy of which is proved to be satisfactory for practical purposes, and an exact solution of this equation is given for wings of very large aspect ratio, swept or unswept. For wings of moderate or small aspect ratios, the solution given fulfills the approximate downwash equation only in the mean over the whole chord, i.e., the downwash is correct not at a few discrete points but on the average. Again, the limiting cases of Jones and Prandtl are included in the present solution. Thus, the load over the whole surface of a given wing can be calculated at a given subcritical Mach number, and the procedure is as simple and rapid as that of the classical aerofoil theory. The calculated results are confirmed by experiment. With this method, the effects of wing thickness and of the boundary layer can easily be taken into account, as well as aero-elastic effects. Non-linearity of the lift due to tip vortices is also treated.